Actually, there is no identified narrator in this story, so it would not be possible to describe one. A story with an identified narrator is written in the first-person point of view; a narrator tells the story as he or she observed or experienced it from a personal point of view. Sometimes the narrator has a name, sometimes not, but the narrator will have an identity, and his or her identity will influence how the story was experienced and then related.

"An Occurrence at Owl Creek Bridge" is written in the third-person point of view. The voice telling the story is not a character with an identity; it is the creative voice of the author telling the story. Sometimes a third-person point of view is limited; the author will limit the details of the story to include only what an observer at the scene would see or hear. Sometimes a third-person point of view is omniscient; the author acts as "all-seeing," and includes not only what could be seen and heard, but also what one or more of the characters is thinking and feeling.

In "An Occurrence at Owl Creek Bridge," Bierce writes from both the limited and the omniscient third-person point of view, moving from one to the other in different parts of the story. For instance, most of part III of the story is written in the third-person omniscient point of view as Bierce takes the reader into Peyton's mind, but the conclusion of the story returns to the third-person limited point of view.

This is an interesting question because the story for the most part is told using the third person point of view. This means that the narrator is an exterior individual to the action and therefore is able to look objectively at what is happening and see the thoughts and feelings of all characters as the story progresses. This is why we see the soldiers as they get ready for the hanging just as clearly as we see Peyton Farquhar himself. However, if I had to imagine what the narrator would look like, I would think that the narrator is some kind of film maker. This is because, at the beginning of the short story, the scene is set and the main character is introduced from without and in a very visual form. Consider the introduction:

A man stood upon a railroad bridge in northern Alabama, looking down into the swift water twenty feet below. The man's hands were behind his back, the wrists bound with a cord. A rope closely encircled his neck. It was attached to a stout cross-timber above his head, and the slack fell to the level of his knees. Some loose boards laid upon the sleepers supporting the metals of the railway supplied a footing for him and his executioners--two private soldiers of the Federal army, directed by a sergeant who in civil life may have been a deputy sheriff.

Note how we are introduced to the scene objectively and dispassionately. Also consider the vivid way in which the details given help us to imagine what this scene would look like. We are given precise information concerning the man who is to be hung and the rope that binds him and the number of men who are with him. This strong visual element is something that is constant throughout the story, and thus I would imagine the narrator to be some kind of movie director. I hope this was what you wanted!